Sparse Linear Solvers

A sparse matrix is a matrix that has relatively few nonzero values. Many engineering and scientific applications require the solution of sparse matrices. Most sparse matrix software takes advantage of this "sparseness" to reduce the amount of storage and arithmetic required by keeping track of only the nonzero entries in the matrix.

IBM provides Sparse Linear Algebraic Equation Subroutines for use on Bassi. The sparse linear algebraic equation subroutines provide direct and iterative solutions to linear systems of equations both for general sparse matrices and their transposes and for sparse symmetric matrices.

For information on available subroutines and their usage see:

• ESSL: Sparse Linear Algebraic Equation Subroutines
• Parallel ESSL: Sparse Linear Algebraic Equation Subroutines

The sparse utility subroutines provided in Parallel ESSL must be used in conjunction with the ESSL sparse linear algebraic equation subroutines.

NAG (bassi and jacquard only)

NAG routines contains iterative methods for symmetric and unsymmetric matrices and direct methods for sparse symmetric positive-definite matrices and sparse unsymmetric matrices. See chapter F11-Sparse Linear Algebra.

PETSc

PETSc, the Portable, Extensible Toolkit for Scientific computation, provides sets of tools for the parallel (as well as serial), numerical solution of PDEs that require solving large-scale, sparse nonlinear systems of equations.

SuperLU

SuperLU is a general purpose library for the direct solution of large, sparse, nonsymmetric systems of linear equations on high performance machines. SuperLU package has three different versions: SuperLU for sequential machines, SuperLU_MT for shared memory parallel machines and SuperLU_DIST for distributed memory.